when we apply it on (REF ), cf. [1]}. Here \(\gamma \)  is a regularization parameter and \(x^{*}\)  is an estimate of the sought-after true solution. In many cases the unregularized problem has a whole set of minimizers, thus the vector \(x^{*}\)  works also as a selection criterion. Now if a reasonable \(x^{*}\)  is found, the regularization parameter \(\gamma \)  can be determined with the discrepancy principle, i.e. \(\gamma \)  is computed such that
\(\Vert \Sigma ^{-\frac{1}{2}}(f_{t}(x_{\gamma }) - f(x_{true}) - \delta )\Vert _{2} = R(\delta ),\) 
